WASHINGTON — As he struggles to sell his nuclear deal with Iran to resistant Republicans and Democrats in Congress, President Obama describes it in the narrowest possible terms, as a limited transaction in which Tehran gives up the bomb in return for sanction relief.

In a conference call with liberal groups on Thursday night, he stuck to his talking points: The principal danger is if the Iranians “get a nuclear weapon, which is exactly what this deal prevents.”

What the president and his aides do not talk about these days — for fear of further antagonizing lawmakers on Capitol Hill who have cast Iran as the ultimate enemy of the United States — are their grander ambitions for a deal they hope could open up relations with Tehran and be part of a transformation in the Middle East.

“Over 15 years, things happen in countries, and if you look at Iran today, very educated, used to be very friendly with a lot of nations in the region, including Israel,” Secretary of State John Kerry said at the Council on Foreign Relations last week. “You know, there’s a long history with Persia. And the reality is that those young people, who are 20 percent unemployed, want a future.”

Administration officials say Mr. Kerry is hopeful that once the nuclear accord is solidified, he will be able to begin talking with the Iranians about ending their support for President Bashar al-Assad of Syria. “Russia and Iran are the two biggest supporters of the regime” in Syria, said a senior administration official, who spoke on condition of anonymity because public comment had not been authorized. Mr. Obama has already spoken to Russia’s president, Vladimir V. Putin, about removing Mr. Assad, the official said.

“There may be an opportunity with Iran as the deal is implemented to pursue a similar conversation,” the official said.

In public, Mr. Obama has played down expectations that the Iran deal could lead to a resolution of the Syrian conflict, saying in a recent White House news conference that Iran was just “one of the players” in the conflict and that he did not “anticipate any time in the near future restored normal diplomatic relations with Iran.”

But the official said the administration would be open to talking with Iran about its battles in Iraq against the Islamic State as the United States fights its own parallel war against the terrorist group.

More broadly, Mr. Obama and his top aides see the possibility of a new equilibrium between Sunni and Shiite groups in the region, a potential shift in alliances that worries America’s closest Arab allies, like Saudi Arabia.

In a press briefing at the White House on Thursday, Josh Earnest, the press secretary, said of the deal, “We’re hopeful that it might result in some kind of change emanating from Iran, but we’re certainly not counting on it.”

Despite White House hopes, many experts say it is naïve to expect that Iran, which provides critical military support to Mr. Assad as well as to the militant group Hezbollah in Lebanon, would be receptive to the administration’s overtures.

“I don’t see any evidence that Iran is increasingly disposed toward facilitating a negotiated solution to the Syrian crisis,” Frederic C. Hof, a former senior State Department official in the Obama administration and now an expert on Syria at the Atlantic Council, told reporters this week. “On the contrary, I think Iran and Hezbollah have been engaged in some very intensive consultations centering on the question of just how much of Assad’s Syria they will defend.”

Before his fight for the deal in Congress, Mr. Obama was far more open about his ultimate goals. In an interview in The Atlantic in March 2014, he said that a nuclear agreement with Iran was a good idea, even if the regime remained unchanged. But an agreement could do far more than that, he said:

“If, on the other hand, they are capable of changing; if, in fact, as a consequence of a deal on their nuclear program those voices and trends inside of Iran are strengthened, and their economy becomes more integrated into the international community, and there’s more travel and greater openness, even if that takes a decade or 15 years or 20 years, then that’s very much an outcome we should desire,” he said.

In a similar vein, Mr. Obama told The New Yorker, “If we were able to get Iran to operate in a responsible fashion — not funding terrorist organizations, not trying to stir up sectarian discontent in other countries, and not developing a nuclear weapon — you could see an equilibrium developing between Sunni, or predominantly Sunni, gulf states and Iran in which there’s competition, perhaps suspicion, but not an active or proxy warfare.”

And in an interview in December, Mr. Obama even seemed to welcome the rise of a powerful Iran. “They have a path to break through that isolation and they should seize it,” he said. “Because if they do, there’s incredible talent and resources and sophistication inside of — inside of Iran, and it would be a very successful regional power.”

The gap between the administration’s quiet ambitions for the deal and its recent public pronouncements has much to do with its assessment about how to sell the deal to Congress between now and September, when Congress is to vote on the accord.

“If they sell this as transformative, and in the immediate term Iran takes more reactionary actions, such as locking up more people, then the administration will be setting themselves up for failure,” said Karim Sadjadpour of the Carnegie Endowment for International Peace. “People will say they’re naïve about the regime.”

Abbas Milani, director of Iranian studies at Stanford University, agreed. “He’s selling it tactically, whereas much of the wisdom of this deal is strategic,” he said. “But that’s because there’s a lot of troubled waters ahead.”

The senior administration official said that Mr. Obama sees the deal as helping ameliorate the “meta-conflict in the Middle East” caused by sectarianism and the rivalry between Saudi Arabia and Iran.

“There is definitely a larger picture here,” the official said.

Robert Satloff, director of the Washington Institute for Near East Policy, said such remarks demonstrate that the nuclear deal is part of “a new grand strategy for America in the Middle East” that Mr. Satloff believes is worrisome.

So while much of the debate over the next two months will be about centrifuges, inspections and whether Iran is actually prevented from getting a nuclear weapon, the administration’s larger strategy is likely to get far less attention. But for administration officials, that long-term strategic bet is at least as important as the short-term nuclear deal, officials said.

“We believe that a world in which there is a deal with Iran is much more likely to produce an evolution in Iranian behavior than a world in which there is no deal,” Benjamin J. Rhodes, the deputy national security adviser, said just before the deal was announced.

Michael R. Gordon contributed reporting.

A version of this article appears in print on , on Page A8 of the New York edition with the headline: Deeper Middle East Aspirations Seen in Obama’s Nuclear Deal With Tehran. Order Reprints | Today’s Paper | Subscribe